Question: Simplify the following expression: $a = \dfrac{8}{z + 5} \div \dfrac{7}{5z}$
Solution: Dividing by an expression is the same as multiplying by its inverse. $a = \dfrac{8}{z + 5} \times \dfrac{5z}{7}$ When multiplying fractions, we multiply the numerators and the denominators. $a = \dfrac{ 8 \times 5z } { (z + 5) \times 7}$ $a = \dfrac{40z}{7z + 35}$